Solving Equation: V0 - dQ(t)/dt * R(t) - Q(t)/C(t)

  • Context: Undergrad 
  • Thread starter Thread starter Mica
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Discussion Overview

The discussion revolves around solving the differential equation V0 - dQ(t)/dt * R(t) - Q(t)/C(t) = 0. Participants explore methods for approaching this equation, including hints and techniques relevant to differential equations.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • Mica seeks assistance in solving the differential equation and asks for hints.
  • One participant inquires about Mica's progress and suggests starting with the homogeneous solution.
  • Mica expresses uncertainty about the form of the differential equation due to a lack of recent experience.
  • Another participant mentions that the equation represents exponential decay.
  • A further contribution describes the equation as a linear differential equation with variable coefficients, noting that the solution is contingent on the specific forms of Q(t) and R(t). They suggest that Laplace Transform might be useful for deriving a formal solution involving integrals of Q(t) and R(t).

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints on how to approach the solution, and no consensus has been reached regarding the best method or the specific forms of Q(t) and R(t).

Contextual Notes

Participants have not clarified the specific definitions or forms of Q(t) and R(t), which may affect the solution approach. There is also a lack of consensus on the steps to take in solving the equation.

Mica
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Hi,

Can someone give me a hint for solving this equation?

V0 - dQ(t)/dt * R(t) - Q(t)/C(t) = 0

Thanks,

Mica
 
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What have you done so far? Have you tried solving the homogeneous solution first?
 
Sorry, I have long time that I did not solve a differencial equation. Can you give me its form?

thanks,

Mica
 
Exponential decay.
 
What you have is a linear differential equation with variable coefficients. The solution depends strongly upon what Q(t) and R(t) are. You might be able to use Laplace Transform to write a "formal" solution in terms of integrals of Q(t) and R(t)
 

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